On the optimisation of a hybrid Tuned Mass Damper for impulse loading

The present paper deals with the optimisation of a hybrid Tuned Mass Damper (TMD) in reducing the transient structural response due to impulse loading. In particular, a unit impulse excitation has been assumed, acting as base displacement, which is a situation that may occur in different real applications. The proposed hybrid Tuned Mass Damper is composed of a previously optimised passive TMD and an added optimised active controller. Such configuration has been conceived in view of reducing both the global and the peak response. Especially on the latter task, the introduction of the active controller brings in a significant contribution. Prior, a Bounded-Input-Bounded-Output (BIBO) stability analysis on the control gains is developed. Different control laws have been investigated, assuming as primary structures, first a single-degree-of-freedom (SDOF) benchmark system and then a multi-degree-of-freedom (MDOF) building, in order to point out the most appropriate control law for the given structural context. In particular, a new control law, based on a linear combination of acceleration and velocity, allowed for remarkable peak response reduction. The achieved dynamic response exhibits a time settling weakly oscillating response, an indication of a stable behaviour, and therefore represents a suitable option for the active controller, in view of various engineering applications.